Can translational invariance of CNNs be unwanted if object is likely in certain positions?
According to your example:

Trees will likely be in the bottom half of the image. Still, you will not know whether there will be one, two or five trees. Thanks to translation invariance property of CNN's, each tree will activate filters responsible for tree detection. You still need to handle those few exceptions where trees are on hill.

To achieve better results in this particular case, you might want to consider some kind of focus mechanism, that will try to get rid of unwanted part of picture, in case when there are (for example) no hills. Take a look at Spatial Transformer Networks. During training it learns to predict spatial transformation (for example zoom) that will help "main" classifier to predict class of image.